Number Of Branch Points Research Articles

Vagotomy Alters Astrocyte Morphology in the Brainstem Nucleus Tractus Solitarii

The nucleus tractus solitarii (nTS) in the brainstem is the initial site of integration and modulation of sensory input from the cardiorespiratory system. The nTS is critical for maintaining blood pressure (BP), heart rate (HR), and respiratory homeostasis, and is an essential part of the reflex response to hypoxia. Alterations in both afferent input and nTS function occur in many cardiorespiratory conditions, including obstructive sleep apnea, hypertension, and heart failure. Visceral sensory information is provided to the nTS, in part, by afferents from the vagus nerves. Vagal afferents activate both neurons and astrocytes to modify nTS output and cardiorespiratory function. Vagotomy has been shown to decrease nTS neuronal activity, but whether this is a direct effect on neurons or indirect due to effects on astrocytes is unknown. We hypothesized that decreased afferent input (vagotomy) modifies nTS astrocyte morphology, and is associated with impaired cardiorespiratory responses to hypoxia. To test this hypothesis, male Sprague‐Dawley rats (5–7 weeks old) underwent either right cervical vagotomy caudal to the nodose (n=8), sham surgery (n=7), or no surgery/control (n=4). Prior to surgery and one week post‐surgery, cardiorespiratory parameters (respiration, oxygen saturation, HR, BP) were measured in conscious and anesthetized animals under baseline and hypoxic conditions (8–12% O2). Rats were euthanized and brains were examined across the caudal‐to‐rostral nTS. Immunohistochemistry was used to evaluate astrocytes with glial fibrillary acidic protein (GFAP) and S100 calcium‐binding protein B (S100B), and glutamatergic synapses with vesicular glutamate transporter 2 (VGLUT2) in the nTS. Immunoreactivity (‐IR) was compared between the left (intact) and right (manipulated) nTS among groups. Vagotomy increased astrocytic GFAP‐IR compared to sham and controls in both the intact and manipulated sides, primarily at the level of the area postrema. Sholl analysis of astrocyte processes showed that vagotomy increased the number of astrocyte branch segments and branchpoints compared to controls on the manipulated side, and both vagotomy and sham increased branching on the manipulated side compared to controls. The latter occurred at unique proximal and distal distances from the cell body. The number of S100B‐IR astrocytes increased in vagotomy (compared to sham) in the intact side, with a trend in the manipulated side. VGLUT2‐IR was not different among groups or between sides, suggesting a similar number of glutamate synapses and lack of their pruning with vagotomy. Cardiorespiratory responses to hypoxia were not altered after vagotomy. These data suggest decreased afferent input increases astrocyte number and morphology, which is likely due to reduced afferent activity rather than presynaptic afferent structural alterations. Thus, afferent input dynamically influences astrocyte structure and likely function to modify neuronal activity, further elucidating the importance of nTS astrocytes in cardiorespiratory homeostasis and disease.Support or Funding InformationT32 OD011126, R01 HL132836, R01 HL128454

Increased number of retinal vessels in acromegaly.

Excess of growth hormone (GH) and insulin-like growth factor 1 (IGF-1), as in acromegaly, is associated with increased risk of diabetes, but whether retinal vessels are altered is unknown. The aim of this study was to evaluate retinal vessel morphology in patients with acromegaly at diagnosis and after treatment and to describe the prevalence of diabetic retinopathy in patients with long-standing acromegaly and diabetes. Two independent observational studies, one being prospective and the other retrospective and cross-sectional. Retinal vessel morphology of 26 patients with acromegaly was examined at diagnosis and 1 year after treatment and compared to 13 healthy controls. Cross-sectional evaluation of 39 patients with long-standing acromegaly and diabetes was performed. Fundus photographs were digitally analyzed for vessel morphology. Patients with acromegaly had a median (interquartile range) of 34.3 (30.0-39.0) vessel branching points compared to 27.0 (24.0-29.0) for healthy controls (P < 0.001). Tortuosity of arterioles and venules remained unchanged. Vessel morphology did not change significantly after treatment. Patients with acromegaly and diabetes for a median of 14 years also had a high number of branching points (34.2 (32.5-35.6)), but the prevalence of diabetic retinopathy was not higher than expected in diabetic patients without acromegaly. Patients with acromegaly have an increased number of vascular branching points in the retina without an alteration of macroscopic vessel morphology. This is consistent with an angiogenic effect of GH/IGF-1 in humans. The prevalence of diabetic retinopathy was not increased in patients with acromegaly and diabetes.

A Resolution of the Poisson Problem for Elastic Plates

We consider the problem of finding a surface \(\Sigma \subset {\mathbb {R}}^m\) of least Willmore energy among all immersed surfaces having the same boundary, boundary Gauss map and area. Such a problem was considered by S. Germain and S.D. Poisson in the early XIX century as a model for equilibria of thin, clamped elastic plates. We present a solution in the case of boundary data of class \(C^{1,1}\) and for when the boundary curve is simple and closed. The minimum is realised by an immersed disk, possibly with a finite number of branch points in its interior, which is of class \(C^{1,\alpha }\) up to the boundary for some \(0<\alpha <1\), and whose Gauss map extends to a map of class \(C^{0,\alpha }\) up to the boundary.

Different patterns in age-related morphometric alteration of myelinated fibers and capillaries of the tibial nerve: a longitudinal study in normal rats.

Age-related regression of myelinated fibers in peripheral nerves of the lower limbs is strongly influenced by capillaries and results in balance dysfunction and falls. However, the temporal relationships between alteration patterns of myelinated fibers and capillaries have not yet been clarified. This study aimed to investigate age-related morphological and histological changes of both myelinated fibers and capillaries in peripheral nerves to clarify whether myelinated fibers or capillaries change earlier. Seven male Wistar rats each were randomly selected at 20weeks (young group), 70weeks (middle group), and 97weeks (old group) for histological evaluations. The left and right tibial nerves were removed morphologically and histologically to examine myelinated fibers and capillaries. Axon diameter and myelin thickness were almost unaltered in the middle group compared with the young group but were significantly reduced in the old group when compared with the other two groups. However, the capillary diameter and number of microvascular branch points were substantially reduced in the middle group. The current study demonstrates that myelinated fibers of peripheral nerves show signs of regression in elderly rats, whereas capillaries start to reduce in middle-aged animals. In normal aging of the tibial nerve, capillaries may regress before myelinated fibers.

Random Branching of Polymer Chains with Schulz–Zimm Distribution. 1. Bivariate Distribution and Related Formulae

AbstractAnalytical solution for the bivariate distribution W(r,k) of the degree of polymerization r and the number of branch points k is obtained for the random branching of polymer chains that follow the Schulz–Zimm distribution, or in mathematical term, the gamma distribution. It is found that when the bivariate distribution is normalized to make the total area unity, the normalized distribution follows another gamma distribution. The bivariate distribution function enables one to determine various useful properties of the branched polymer system, including full weight fraction distribution W(r), the number‐ and weight‐average degree of polymerization having k branch points, the expected branching density ρ for a given degree of polymerization r or a given number of branch points k. The branching density at large r limit, ρr → ∞ is an important property to represent the branched polymer system, rather than the average branching density of the whole system, and the value of ρr → ∞ can be determined for the present random branched system. The effect of the distribution breadth of the primary chains can be investigated by using the formulae developed in this article.

Random Branching of Polymer Chains with Schulz–Zimm Distribution. 2. Radius of Gyration and Maximum Span Length

AbstractMean‐square radius of gyration Rg2 and the maximum span length LMS of each polymer molecule are investigated for the random branching of primary chains that follow the Schulz–Zimm distribution, by using the Monte Carlo simulation method. It is found that the expected g‐ratio of Rg2 of the branched molecule to that of a linear molecule for a given number of branch points k does not change with the branching density. The expected g‐ratio becomes larger for the primary chains with broader distribution. An approximate formula for the relationship between g‐ratio and k that accounts for the distribution breadth is proposed. The relationship between the weight fraction of the maximum span chain LMS/(degree of polymerization) and k shows the analogous behavior with that for g‐ratio and k. The magnitude of Rg2 is proportional to LMS, with Rg2 = 0.18 LMS, irrespective of the breadth of the primary polymer chain length distribution.

Abstract TP470: Stimulation of Blood Vessel Formation by Human Neural Stem/Progenitor Cells is Mediated by Secreted Material

Human neural stem/progenitor cells (hNSPCs) have the potential to widen the current narrow treatment window for stroke as they improve functional recovery in rodent stroke models when transplanted weeks after stroke. One aspect of the hNSPC-induced functional recovery is increased angiogenesis and neovascularization in the peri-infarct region. Our lab created a human cell in vitro model of vessel formation by seeding hNSPCs and human endothelial progenitor cells (hEPCs) in a 3D scaffold composed of salmon fibrinogen, laminin, and hyaluronic acid that mimics brain tissue properties. Using our in vitro neurovascular model, we tested the hypothesis that hNSPC-secreted material plays a role in the stimulation of vessel formation. Our RNA-Seq data show that hNSPCs express high levels of secreted pro-angiogenic proteins, such as growth factors, matrix molecules, and cytokines, but hNSPCs might also impact vessel formation by secretion of extracellular vesicles or cell-contact mediated mechanisms. In order to determine the effect of hNSPC-secreted material on vessel formation, mCherry-labeled hEPCs were seeded in 3D scaffolds alone, with CellTracker Green-labeled hNSPCs, or with hNSPC-conditioned media containing hNSPC-secreted soluble factors and extracellular vesicles, such as exosomes. Vessel formation was quantified using AngioTool to determine total vessel length, number of branch points, and vessel percentage area. We found an increase in vessel formation in the presence of hNSPCs and hNSPC-conditioned media compared to hEPCs alone. In conclusion, material secreted by hNSPCs can recapitulate the increase in vessel formation induced by hNSPCs themselves. In future studies, we will determine whether hNSPC-derived exosomes are important for promoting vessel formation as they have therapeutic potential without the limitations of cell therapy.

Abstract WP137: Time-Course Characterization of Blood-Brain Barrier Disruption in Secondary Thalamic Injury After Stroke

Introduction: A secondary degenerative injury occurs in the thalamus after primary cortical ischemic stroke. This secondary thalamic injury progresses long-term and is associated with somatosensory dysfunctions. Blood-brain barrier (BBB) disruption is one of the feature pathological changes in primary ischemic stroke, but whether BBB disruption happens in the secondary thalamic injury is unclear. In this study, we aim to investigate the BBB changes during the development of secondary thalamic injury after stroke. Methods: Cortical ischemic stroke was generated by permanent occlusion of the left middle cerebral artery on male C57BL6J mice (12-15 weeks). BBB permeability was assessed by Biocytin-TMR (869 Da, 1mg/mL) at post-stroke days (PD) 1, 3, 7, 14, 28, 56, and 84. Immunostainings of CD68 (inflammation) and CD31 (vascular morphology) were performed. Brain sections were imaged with Confocal LSM800 and quantified by NIH ImageJ and Wimasis Image Analysis. BBB permeability related genes were quantified by real-time PCR among naïve, PD7 and PD28. Results: In ipsilesional thalamus (iTH), the Biocytin-TMR was detected as early as PD3 in the secondary thalamic injury area and persisted until at least PD84. The fluorescence intensity of Biocytin-TMR significantly increased during PD28-84 and peaked at PD56, suggesting the BBB is chronically disrupted in iTH. Compared to naïve animals, stroke animals exhibited significant increase in tube length, total number of tubes and total number of branching points at PD56 and PD84. mRNA expression of ZO-2 significantly down-regulated at PD7 and returned to baseline levels by PD28. mRNA of Angiopoietin-1 ( Ang-1 ), VEGFa and Adam10 were significantly increased at PD28. Conclusion: Our data demonstrate that the BBB disruption begins early at PD3 and continues to progress until PD84 in the secondary degenerative thalamus. This BBB disruption is accompanied by changes in blood vessel morphology and permeability related genes. Current studies are examining the expression of key genes at PD56 using qPCR and immunohistochemistry. Our results will elucidate the cellular and molecular changes of BBB disruption involved in thalamic injury, which will provide potential targets for enhancing stroke recovery.

The depths and the attracting centres for continuous maps on local dendrites with the number of branch points being finite

Let Y be a local dendrite with the number of branch points being finite and f : Y → Y be continuous. Denote by P ( f ) , R ( f ) , Ω ( f ) and ω ( x , f ) the set of periodic points of f , the set of recurrent points of f , the set of non-wandering points of f and the set of ω -limit points of x under f , respectively. Write ω ( f ) = ∪ x ∈ Y ω ( x , f ) and ω n + 1 ( f ) = ∪ x ∈ ω n ( f ) ω ( x , f ) and Ω n + 1 ( f ) = Ω ( f | Ω n ( f ) ) for any positive integer n . In this paper, we show that Ω 3 ( f ) = R ( f ) ‾ and the depth of f is at most 3, and ω 3 ( f ) = ω 2 ( f ) . Furthermore, we show that R ( f ) ‾ = R ( f ) ∪ P ( f ) ‾ .

Characteristic of pointwise-recurrent maps on a dendrite

Let f be a continuous map on a dendrite D with f (D) = D. Denote by R(f ) and AP (f ) the set of recurrent points and the set of almost periodic points of f , respectively, and denote by ω(x, f ), Λ(x, f ), Γ(x, f ) and Ω(x, f ) the set of ω-limit points, the set of α-limit points, the set of γ-limit points and the set of weak ω-limit points of x under f , respectively. In this paper, we show that the following statements are equivalent: (1) D = R(f ). (2) D = AP (f ). (3) Ω(x, f ) = ω(x, f ) for any x ∈ D. (4) Ω(x, f ) = Γ(x, f ) for any x ∈ D. (5) f is equicontinuous. (6) [c, d] ⊄ Ω(x, f ) for any c, d,x ∈ D with c ≠ (7) Ω(x, f ) is minimal for any x ∈ D. (8) Card(Λ − 1(x, f ) ∩ (D−End(D))) < ∞ for any x ∈ D, where Λ − 1(x, f ) = {y : x ∈ Λ(y, f )}, End(D) is the set of endpoints of D and Card(A) is the cardinal number of set A. (9) If x ∈ Λ(y, f ) with x, y ∈ D, then y ∈ ω(x, f ). (10) Map h : x → ω(x, f ) (x ∈ D) is continuous and for any x, y ∈ D with x ∉ ω(y, f ), ω(x, f ) ≠ ω(y, f ). Besides, we also study characteristic of pointwise-recurrent maps on a dendrite with the number of branch points being finite.

Antiangiogenic activity of zinc and zinc-sorafenib combination using the chick chorioallantoic membrane assay: A descriptive study.

Zinc, a trace element, is known for downregulating several proangiogenic growth factors and cytokines. However, its antiangiogenic activity is not adequately studied. The present study was aimed to evaluate the possible antiangiogenic activity of zinc via the chick chorioallantoic membrane (CAM) assay. Furthermore, the antiangiogenic activity of the combination therapy of zinc with various doses of sorafenib, a tyrosine kinase inhibitor, was evaluated. A pilot study was initially conducted so as to select suitable doses of zinc and sorafenib. The antiangiogenic activity after combining zinc 2.5 μg/embryo with sorafenib 1 and 2 μg/embryo was also evaluated. The antiangiogenic activity was quantified in terms of total length of blood vessels, number of junctions, number of branching points, and mean length of the blood vessels. Zinc 2.5 μg/embryo showed significant (P < 0.05) antiangiogenic activity, as compared to the control group. However, its effect was not comparable to that of sorafenib 2 μg/embryo. The combination of zinc 2.5 μg/embryo with sorafenib 2 μg/embryo did not show an additive/synergistic effect. The combination of zinc 2.5 μg/embryo with sorafenib 1 μg/embryo produced an antiangiogenic activity which was comparable (P > 0.05) to that of sorafenib 2 μg/embryo. Zinc caused significant antiangiogenic activity in the CAM assay. The lack of addition/synergism in the zinc-sorafenib combination could have been due to the variability in the dose/ratio selection. Addition of zinc to sorafenib therapy could improve treatment tolerability, reduce cost of therapy, and reduce the emergence of drug resistance. Future mechanistic studies could identify the exact pharmacodynamics of zinc as an angiogenesis inhibitor.

Global bifurcation for the Hénon problem

We prove the existence of nonradial solutions for the Henon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent \begin{document}$ \alpha $\end{document} . For sign-changing solutions, the case \begin{document}$ \alpha = 0 $\end{document} -Lane-Emden equation- is included. The obtained solutions form global continua which branch off from the curve of radial solutions \begin{document}$ p\mapsto u_p $\end{document} , and the number of branching points increases with both the number of nodal zones and the exponent \begin{document}$ \alpha $\end{document} . The proof technique relies on the index of fixed points in cones and provides information on the symmetry properties of the bifurcating solutions and the possible intersection and/or overlapping between different branches, thus allowing to separate them in some cases.

Hybrid DNA/RNA nanostructures with 2'-5' linkages.

Nucleic acid nanostructures with different chemical compositions have shown utility in biological applications as they provide additional assembly parameters and enhanced stability. The naturally occurring 2'-5' linkage in RNA is thought to be a prebiotic analogue and has potential use in antisense therapeutics. Here, we report the first instance of DNA/RNA motifs containing 2'-5' linkages. We synthesized and incorporated RNA strands with 2'-5' linkages into different DNA motifs with varying number of branch points (a duplex, four arm junction, double crossover motif and tensegrity triangle motif). Using experimental characterization and molecular dynamics simulations, we show that hybrid DNA/RNA nanostructures can accommodate interspersed 2'-5' linkages with relatively minor effect on the formation of these structures. Further, the modified nanostructures showed improved resistance to ribonuclease cleavage, indicating their potential use in the construction of robust drug delivery vehicles with prolonged stability in physiological conditions.

Characterizing the interplay between gene nucleotide composition bias and splicing

BackgroundNucleotide composition bias plays an important role in the 1D and 3D organization of the human genome. Here, we investigate the potential interplay between nucleotide composition bias and the regulation of exon recognition during splicing.ResultsBy analyzing dozens of RNA-seq datasets, we identify two groups of splicing factors that activate either about 3200 GC-rich exons or about 4000 AT-rich exons. We show that splicing factor–dependent GC-rich exons have predicted RNA secondary structures at 5′ ss and are dependent on U1 snRNP–associated proteins. In contrast, splicing factor–dependent AT-rich exons have a large number of decoy branch points, SF1- or U2AF2-binding sites and are dependent on U2 snRNP–associated proteins. Nucleotide composition bias also influences local chromatin organization, with consequences for exon recognition during splicing. Interestingly, the GC content of exons correlates with that of their hosting genes, isochores, and topologically associated domains.ConclusionsWe propose that regional nucleotide composition bias over several dozens of kilobase pairs leaves a local footprint at the exon level and induces constraints during splicing that can be alleviated by local chromatin organization at the DNA level and recruitment of specific splicing factors at the RNA level. Therefore, nucleotide composition bias establishes a direct link between genome organization and local regulatory processes, like alternative splicing.

Effects of mesencephalic astrocyte-derived neurotrophic factor on cerebral angiogenesis in a rat model of cerebral ischemia

Mesencephalic astrocyte-derived neurotrophic factor (MANF) is an endoplasmic reticulum stress-related protein that exhibits neuroprotective effects. Recent studies have shown that MANF promotes poststroke functional recovery in rats. However, the underlying mechanisms have not yet been fully understood. Here, we examined the effects of MANF on cerebral angiogenesis in a permanent middle cerebral artery occlusion model in rats. Recombinant human MANF was administered intracerebroventricularly 24 h after stroke. We performed neurobehavioral tests and assessed microvessel density, functional microvessels, and regional cerebral blood flow (rCBF), as well as detected angiogenic factors in the peri-infarct cerebral cortex. Results showed that MANF ameliorated neurobehavioral scores, promoted rCBF, upregulated the expression of CD34, as well as the total vessel surface area and the number of microvessel branch points, and activated the vascular endothelial growth factor (VEGF) pathway. In conclusion, our findings provide insight into the mechanisms of MANF in promoting functional recovery from ischemic stroke. Our results suggest that MANF improves neurobehavioral recovery from cerebral ischemic injury, and that this effect is mediated partly by its proangiogenic effects and augmentation of rCBF, which are possibly associated with VEGF.

Overlapping morphological and functional properties between M4 and M5 intrinsically photosensitive retinal ganglion cells.

Multiple retinal ganglion cell (RGC) types in the mouse retina mediate pattern vision by responding to specific features of the visual scene. The M4 and M5 melanopsin-expressing, intrinsically photosensitive retinal ganglion cell (ipRGC) subtypes are two RGC types that are thought to play major roles in pattern vision. The M4 ipRGCs overlap in population with ON-alpha RGCs, while M5 ipRGCs were recently reported to exhibit opponent responses to different wavelengths of light (color opponency). Despite their seemingly distinct roles in visual processing, previous reports have suggested that these two populations may exhibit overlap in their morphological and functional properties, which calls into question whether these are in fact distinct RGC types. Here, we show that M4 and M5 ipRGCs are distinct morphological classes of ipRGCs, but they cannot be exclusively differentiated based on color opponency and dendritic morphology as previously reported. Instead, we find that M4 and M5 ipRGCs can only be distinguished based on soma size and the number of dendritic branch points in combination with SMI-32 immunoreactivity. These results have important implications for clearly defining RGC types and their roles in visual behavior.

An artificial intelligence-based deep learning algorithm for the diagnosis of diabetic neuropathy using corneal confocal microscopy: a development and validation study

Aims/hypothesisCorneal confocal microscopy is a rapid non-invasive ophthalmic imaging technique that identifies peripheral and central neurodegenerative disease. Quantification of corneal sub-basal nerve plexus morphology, however, requires either time-consuming manual annotation or a less-sensitive automated image analysis approach. We aimed to develop and validate an artificial intelligence-based, deep learning algorithm for the quantification of nerve fibre properties relevant to the diagnosis of diabetic neuropathy and to compare it with a validated automated analysis program, ACCMetrics.MethodsOur deep learning algorithm, which employs a convolutional neural network with data augmentation, was developed for the automated quantification of the corneal sub-basal nerve plexus for the diagnosis of diabetic neuropathy. The algorithm was trained using a high-end graphics processor unit on 1698 corneal confocal microscopy images; for external validation, it was further tested on 2137 images. The algorithm was developed to identify total nerve fibre length, branch points, tail points, number and length of nerve segments, and fractal numbers. Sensitivity analyses were undertaken to determine the AUC for ACCMetrics and our algorithm for the diagnosis of diabetic neuropathy.ResultsThe intraclass correlation coefficients for our algorithm were superior to those for ACCMetrics for total corneal nerve fibre length (0.933 vs 0.825), mean length per segment (0.656 vs 0.325), number of branch points (0.891 vs 0.570), number of tail points (0.623 vs 0.257), number of nerve segments (0.878 vs 0.504) and fractals (0.927 vs 0.758). In addition, our proposed algorithm achieved an AUC of 0.83, specificity of 0.87 and sensitivity of 0.68 for the classification of participants without (n = 90) and with (n = 132) neuropathy (defined by the Toronto criteria).Conclusions/interpretationThese results demonstrated that our deep learning algorithm provides rapid and excellent localisation performance for the quantification of corneal nerve biomarkers. This model has potential for adoption into clinical screening programmes for diabetic neuropathy.Data availabilityThe publicly shared cornea nerve dataset (dataset 1) is available at http://bioimlab.dei.unipd.it/Corneal%20Nerve%20Tortuosity%20Data%20Set.htm and http://bioimlab.dei.unipd.it/Corneal%20Nerve%20Data%20Set.htm.

DENSITY RESULTS FOR SPECIALIZATION SETS OF GALOIS COVERS

AbstractWe provide evidence for this conclusion: given a finite Galois cover $f:X\rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$ of group $G$, almost all (in a density sense) realizations of $G$ over $\mathbb{Q}$ do not occur as specializations of $f$. We show that this holds if the number of branch points of $f$ is sufficiently large, under the abc-conjecture and, possibly, the lower bound predicted by the Malle conjecture for the number of Galois extensions of $\mathbb{Q}$ of given group and bounded discriminant. This widely extends a result of Granville on the lack of $\mathbb{Q}$-rational points on quadratic twists of hyperelliptic curves over $\mathbb{Q}$ with large genus, under the abc-conjecture (a diophantine reformulation of the case $G=\mathbb{Z}/2\mathbb{Z}$ of our result). As a further evidence, we exhibit a few finite groups $G$ for which the above conclusion holds unconditionally for almost all covers of $\mathbb{P}_{\mathbb{Q}}^{1}$ of group $G$. We also introduce a local–global principle for specializations of Galois covers $f:X\rightarrow \mathbb{P}_{\mathbb{Q}}^{1}$ and show that it often fails if $f$ has abelian Galois group and sufficiently many branch points, under the abc-conjecture. On the one hand, such a local–global conclusion underscores the ‘smallness’ of the specialization set of a Galois cover of $\mathbb{P}_{\mathbb{Q}}^{1}$. On the other hand, it allows to generate conditionally ‘many’ curves over $\mathbb{Q}$ failing the Hasse principle, thus generalizing a recent result of Clark and Watson devoted to the hyperelliptic case.

Self-assembly of core-corona particles confined in a circular box

Using Monte Carlo simulations, we study the assembly of colloidal particles interacting via isotropic core-corona potentials in two dimensions and confined in a circular box. We explore the structural variety at low temperatures as function of the number of particles (N) and the size of the confining box and find a rich variety of patterns that are not observed in unconfined flat space. For a small number of particles , we identify the zero-temperature minimal energy configurations at a given box size. When the number of particles is large (), we distinguish different regimes that appear in route towards close packing configurations as the box size decreases. These regimes are characterized by the increase in the number of branching points and their coordination number. Interestingly, we obtain anisotropic open structures with unexpected variety of rotational symmetries that can be controlled by changing the model parameters, and some of the structures have chirality, in spite of the isotropy of the interactions and of the confining box. For arbitrary temperatures, we employ Monte Carlo integration to obtain the average energy and the configurational entropy of the system, which are then used to construct a phase diagram as function of temperature and box radius. Our findings show that confined core-corona particles can be a suitable system to engineer particles with highly complex internal structure that may serve as building blocks in hierarchical assembly.

The protein tyrosine phosphatase PTPRJ/DEP-1 contributes to the regulation of the Notch-signaling pathway and sprouting angiogenesis.

The Dll4-Notch-signaling pathway regulates capillary sprouting via the specification of endothelial tip cells. While VEGF is a potent inducer of Dll4 expression, the intracellular mediators that stimulate its expression remain poorly defined. The protein tyrosine phosphatase PTPRJ/DEP-1 is required for angiogenesis in normal or pathological contexts through its modulation of VEGF signaling. Here, we show that in DEP-1 KO mice, retinas at post-natal day 5 show enlarged blood vessels, as well as an increased number of tip cells and vessel branching points at the migrating front of the vascular plexus. Consistent with these observations, the proliferation of endothelial cells is increased in the retinas of DEP-1 KO mice, as revealed by phospho-histone H3 staining, and increased phosphorylation of ERK1/2 in HUVECs transfected with DEP-1 siRNA. The expression of Dll4 was decreased in retinas of DEP-1 KO mice and was associated with decreased Notch activation. Mechanistically, reduced Dll4 expression in the absence of DEP-1 was correlated with the inhibition of the Src/Akt/β-Catenin-signaling pathway in HUVECs. Conversely, overexpression of WT DEP-1 in cultured endothelial cells, but not of mutants unable to activate Src-dependent signaling, promoted Dll4 expression. Inhibition of Src, Akt, and β-catenin transcriptional activity, leading to the inhibition of Dll4 expression, further suggested that their activation through a DEP-1-dependent pathway was required to promote Dll4 expression in VEGF-stimulated endothelial cells. Altogether, these data demonstrate that DEP-1, via Akt and β-catenin, is a significant promoter of the VEGF-induced Dll4-Notch pathway, and can contribute to the regulation of the tip and stalk cell phenotypes of endothelial cells.